Finding an Elementary Matrix E for A and B

[ephemeral1]

Homework Statement

A= 1 2 -3 B= -1 2 0
0 1 2 0 1 2
-1 2 0 1 2 -3

Find an elementary matrix E such that EA=B

Homework Equations

None

The Attempt at a Solution

I don't know how to start this problem. Please help. Thank you.

 

[rsa58]

the elementary matrix that you want is gotten by taking the identity matrix and interchanging the first and third column. this emulates the interchanging of the corresponding rows in A. As we would expect elementary matrices are invertible so we can make operations on the matrix in both directions retracing our steps or continuing until we reach a certain form. in numerical linear algebra these matrices (along with certain conditions which ensure a minimum of error in the computations) are used to solve systems of linear equations. if you want to check it out look up the LU factorization.

 

[vela]

Homework Statement

$$A=\begin{pmatrix}1 & 2 & -3 \\ 0 & 1 & 2 \\ -1 & 2 & 0\end{pmatrix}B=\begin{pmatrix}-1 & 2 & 0 \\ 0 & 1 & 2 \\ 1 & 2 & -3\end{pmatrix}$$

Find an elementary matrix E such that EA=B.

I don't know how to start this problem.

First, what are the elementary row operations? Second, how are they represented by matrices?

 

[rsa58]

since this question is basically trivial the answer is given by (0 0 1;0 1 0; 1 0 0). plug this into the equation to verify the result. try solving a system of linear equations. the steps that you take in this process are called elementary operations. giving your problem a context i think is important.